## Precalculus (6th Edition) Blitzer

The required value of the tan 2B is $\frac{2\tan \,B}{1-{{\tan }^{2}}B}$.
In order to find the value of tan 2B, the double angle formula is used: $\tan \left( \alpha +\beta \right)=\frac{\tan \alpha +\tan \beta }{1-\tan \alpha \tan \beta }$ Now, consider $\alpha$ and $\beta$ as B; then the formula becomes: \begin{align} & \tan \left( B+B \right)=\frac{\tan B+\tan \,B}{1-\tan B\tan B} \\ & =\frac{2\tan \,B}{1-{{\tan }^{2}}B} \end{align} Hence, the required value of tan 2B is $\frac{2\tan \,B}{1-{{\tan }^{2}}B}$.